A new mesh optimisation scheme, reduced order mesh optimisation, is introduced. The technique uses proper orthogonal decomposition to reduce the number of dimensions in a mesh optimisation problem. This reduction in dimensionality allows the expression of the optimisation problem globally rather than the more traditional local mesh optimisation or smoothing algorithms. To perform the optimisation, the recently developed gradient-free technique modified cuckoo search is applied. The effectiveness of the algorithm is shown by considering the problem of optimising meshes for use in co-volume techniques. Co-volume techniques require the existence of two mutually orthogonal meshes; this is achieved by utilising the Delaunay–Voronoi dual. A combination of considering the problem globally and the use of a gradient-free technique results in a scheme that significantly outperforms previous methods in solving this particular problem. Although the examples presented in this paper are specific to optimising dual meshes, the technique is general and can be simply modified to any mesh optimisation problem. Copyright © 2012 John Wiley & Sons, Ltd.